All Compact Orientable Three Dimensional Manifolds Admit Total Foliations

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American Mathematical Society, 1980 - Mathematics - 74 pages
A total foliation is an example of a geometric structure on a manifold. A total foliation of an [script]n dimensional manifold consists of a [script]n codimension one foliations that are transverse at every point. If a manifold admits a total foliation where all [script]n foliations are transverse oriented, it is said to be totally parallelizable. A necessary condition for total parallelizability is that the manifold be parallelizable. Whether or not this is also a sufficient condition is not known. In this memoir, the author proves a theorem: All compact orientable three dimensional manifolds admit total foliations. This theorem is proven by explicitly constructing total foliations for all compact orientable three manifolds

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